Dont spoil your holiday by going to early, I went last year to check on my apartment the last week in April, when I was returing (1 May) I was told my loads of bulgarians that the official season open, for them anyway, is the first weekend in May...
whe I was there in May alot of the pools were not filled up and only Djannys and the Condor restaurants in SB were open, the beach was desolate and it was not hot.
Like The UK, Sunny Beach has bitter winters...
This being said I would not go until the last week in May at the earliest - this year Im going first week in June
Sunny Beach can be very busy and 18-30 ish in peak season so it depends what your looking for
My personal opinion? First 2 weeks in June
Bubba